Counter-terror police are investigating three packages containing explosives found at Heathrow Airport, London City Airport and Waterloo station.
The "small improvised explosive devices" were found in A4 postal bags, the Metropolitan Police said.
The force's Counter Terrorism Command is treating it as a "linked series" and "keeping an open mind" about motives.
Irish police are assisting the Met as the Heathrow and Waterloo packages had Republic of Ireland stamps.
Heathrow's Compass Centre was evacuated after a package was reported to police at about 09:55 GMT.
The device caught fire when staff opened the bag.
Scotland Yard said: "The packages - all A4-sized white postal bags containing yellow Jiffy bags - have been assessed by specialist officers to be small improvised explosive devices.
"These devices, at this early stage of the investigation, appear capable of igniting an initially small fire when opened."
A Heathrow spokeswoman said the airport would support the police investigation into the "criminal act".
The Gardaí confirmed it was also assisting the Met.
Ireland's postal service identified the stamps as its "Love & Wedding" design for greeting cards, wedding invitations and thank-you cards.
The Compass Centre, which is an office for Heathrow staff rather than part of the passenger terminals, remains closed.
The picture of the jiffy bag addressed to Waterloo appears to show its sender's address as Bus Eireann, Dublin.
The operator said police had not been in touch, with a spokeswoman saying: "Bus Eireann are currently not aware of this and we have no further comment."
Analysis: BBC News Home Affairs Correspondent Daniel Sandford
Working explosive devices being sent through the mail - or letter bombs - are very rare in the UK.
Fortunately these packages only appear to be designed to start a very small fire - the one that went off just melted part of its own plastic envelope, and the other two were not opened.
But there is sufficient concern about today's incidents for them to be investigated as a linked series by Scotland Yard's Counter Terrorism Command.
This means the full weight of resources and expertise of one of the world's most experienced counter terrorism teams will be trying to get to the bottom of who sent the packages and why.
The motive is unclear. It could be anything from Irish republicanism to a grievance against transport companies. Other possibilities include someone with strong opinions about Brexit or someone with mental health problems.
The devices do not seem to be capable of causing serious injury, so they were probably intended to have a nuisance effect and to generate publicity, which they have successfully done.
Police will be hoping the series is now over.
Two more packages were found in the capital over the next three hours.
An area of Waterloo station was cordoned off after a second package was discovered in the post room at about 11:40, the BBC understands.
One worker among a group of staff outside the Network Rail office said he found the package.
Asked about the discovery, he said: "I'm sorry, I've been told I can't talk about it."
About 100 workers were evacuated from City Aviation House at City Airport in Newham after a third package was reported at about 12:10.
City Aviation House is a two-minute walk from the passenger terminal.
Staff returned to the office at about 16:00.
The second and third packages were not opened and have since been "made safe", police said.
Flights were not affected but Docklands Light Railway trains did not stop at City Airport for about an hour during the investigation.
Assistant Chief Constable Sean O'Callaghan, from British Transport Police, said commuters should feel "safe and reassured" while travelling.
"Officers will be highly visible on station concourses, on board trains as well as the London Underground network," he added.
"Passengers are of course the eyes and ears of the network and we want to hear from you if you see something that doesn't look right."
Transport Secretary Chris Grayling urged people to report "anything suspicious" to police, while Mayor of London Sadiq Khan added: "Our thanks go to police, security, transport staff and all involved for their swift actions to keep our city safe."
The @metpoliceuk Counter Terrorism Command has launched an investigation after three suspicious packages were found at locations in London.— Sadiq Khan (@SadiqKhan) March 5, 2019
Our thanks go to police, security, transport staff and all involved for their swift actions to keep our city safe.https://t.co/Ow7xxILfRs